All Questions
Tagged with integer-programming algorithms
18 questions
3
votes
1
answer
368
views
Lot sizing problem: how to add these cuts efficiently
Consider the set of constraints of the uncapacitated lot sizing problem:
$$
\{(x,s,y)\in \mathbb{R}^n_+ \times \mathbb{R}^n_+ \times \mathbb{B}^n \;|\;s_{t-1}+x_t = d_t+s_t,\; x_t \le My_t,\; t=1,\...
CommunityBot
- 1
2
votes
0
answers
95
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Why cannot we adapt Barvinok type counting techniques to general convex integer programs?
Decision problems in Integer Linear Programming have Lenstra type algorithms (https://www.math.leidenuniv.nl/~lenstrahw/PUBLICATIONS/1983i/art.pdf) have been generalized to convex integer program ...
- 13.9k
0
votes
1
answer
82
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Algorithm to find a number B with same modulus as A with prime P and specific binary positions set to zero
Given a prime $P$, an integer $A$ $(0\leq A<P$), and a set of legal positions (encoded as a binary mask $\text{mask}$), is there an efficient algorithm to find a number $B$ that has the same ...
- 5,429
4
votes
0
answers
104
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Questions in number theory related to $NC$ and $P$-completeness
Given $a,b\in\mathbb N$ find $\operatorname{GCD}(a,b)$.
Given $a,b,c\in\mathbb N$ find $x,y\in\mathbb Z$ such that $ax+by=c$.
Euclidean algorithm solves both.
My question is if either 1 or 2 is in ...
1
vote
1
answer
303
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Is this variant of knapsack problem strongly NP-hard?
Suppose we have a sequence of containers each of which contains multiple items. Each item $I_i$ is associated with an nonnegative weight $w_i$, a nonnegative value $v_i$, and $I_i(C)$ denotes the ID ...
- 4,219
1
vote
1
answer
253
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Knapsack problem with capacity constraint
The traditional knapsack problem is that: given a sequence of $i$ items with positive weights $w_1,w_2,...,w_i$, positive values $v_1,v_2,...,v_i$, and a bag with capacity $B$, we want to insert items ...
- 2,504
-1
votes
1
answer
103
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How to solve MILP problem on several linear subspaces
I have a set of close mixed-integer programming problems. More exactly, all the problems share the same set of (binary and continuous) variables, the same set of linear inequality constraints, and the ...
- 5,429
4
votes
1
answer
2k
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Under what conditions does an Integer Programming problem run in polynomial time?
Given $AX\leq B$ where $A\in\Bbb Z^{m\times n}$,$B\in\Bbb Z^m$ finding $X\in\Bbb Z^n$ where $m\geq n$ is the integer programming problem. If $A$ is totally unimodular then the problem is solvable in ...
CommunityBot
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3
votes
1
answer
198
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Separation of Anti-Hole Inequality
Given an undirected graph $G=(V,E)$ with no loops or multiple edges, a stable set is a set of vertices for which no two vertices are adjacent.
An induced subgraph $H$ of $G$ is called an odd-antihole ...
- 151k
6
votes
1
answer
263
views
Algorithm that solves every Mixed Integer Linear Program (to optimality)?
Given a Mixed Integer Linear Program with rational coefficients (both for the objective functions and all constraints), is it always possible to solve it algorithmically?
I know that you usually ...
- 2,464
2
votes
2
answers
202
views
Combinatorial optimization problem involving infinite spin system
In material science research, I am developing an algorithm to solve an infinite combinatorial optimization problem which I believe is the most natural problem when the system size goes to infinity.
...
2
votes
1
answer
1k
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Finding integer points inside of a parallelogram
Suppose $P = \{p_1,\ldots,p_4\} \in \mathbb{R}^2$ defines a quadrilateral (here, specifically, a parallelogram). In the particular case I'm dealing with, I know that there exists at least one point ...
- 12.3k
3
votes
0
answers
350
views
Beating Kadane's Algorithm
I am seeking some reference on already existing work for the following problem.
Given an $n$-dimensional square matrix $A=DP$ where $D$ is a diagonal and $P$ is a permutation matrix (think of Gaussian ...
1
vote
1
answer
3k
views
Multiple disjoint subset sum problem
Given two sets of nonnegative integer numbers:
$X = {x_1, x_2, ... x_n}$
$Y = {y_1, y_2, ... y_m}$
Need to find partition of $X$ on $m$ disjoint subsets, such as sum of elements in $i$-th subset ...
CommunityBot
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1
vote
0
answers
418
views
Maximum subset of set of Integers with minimum distance
Hi, i have a set of integers for example: {0,1,3,100,102} and i am looking for a maximum subset in which all elements have a minimum distance to all elements (or the "next" doesnt matter i guess) for ...
- 41
4
votes
0
answers
392
views
Matching a binary matrix
Given a MxN 0-1 matrix D, with the property that
both M and N are odd numbers
its row sums and column sums in the $\mathbb{Z}_2$ field are all equal to the same number (0 or 1).
How do we find M ...
- 167
4
votes
0
answers
242
views
Domination in Nice Lattices
Let an integer vector be nice when it has only two nonzero components, which sum to zero. So (0, 0, 3, 0, -3) and (-1, 0, 1, 0, 0) are examples of nice vectors in $n=5$ dimensions.
Call a lattice ...
CommunityBot
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2
votes
3
answers
419
views
On special type polynomial inequalities over integers
A special monomial is a monomial of the form $C\cdot x_{i_1} \cdot \ldots \cdot x_{i_n}$, where C is an integer and no variable is repeated more than once in the monomial. For instance, $x\cdot y\cdot ...
- 156k